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Dupit’s Formula for Steady One Directional and Equilibrium Radical Flow

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Read this article to learn about the Dupit’s formula for steady one directional and equilibrium radical flow.

Dupit’s Formula for Steady One Directional Flow:

The steady flow of groundwater in a confined aquifer of uniform thickness behaves in accordance with Darcy’s law; that is, the head decreases Linearly in the direction of flow. However, in a free aquifer the water table is also a flow line. The shape of the water table determines the flow distribution conversely, the flow distribution determines the shape of the water table. Therefore, general analytical solution of the flow is not possible.

However, Dupit in an attempt to simplify analysis of un-directional flow, made the following assumptions:

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1. The velocity of flow is proportional to the tangent of the hydraulic gradient rather than the sine as determined by Darcy; and

2. The flow is horizontal and uniform everywhere in a vertical section.

Dupit derived the following equation:

Q = K (h22 – h12)/2L

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Where, Q = flow of water per unit time, per unit width normal to the direction of flow.

h1 = head of water in the aquifer at point 1 in the line of flow.

h2 = head of water in the aquifer at point 2 in the line of flow from h1 and

L = distance between the points 1 and 2 parallel to the direction of flow.

Despite the simplifying assumptions, the equation closely approximates the water table position where the sine and tangent of the slope of the water table are approximately equal.

Dupit’s Formulas for Steady or Equilibrium Radial Flow:

In 1863 Dupit analysed steady or equilibrium flow in gravity wells as well as pressure wells sunk in unconfined and confined aquifers. He studied a single well in which steady state or equilibrium condition was established by pumping the water from the well for a sufficiently long time till the rate of pumping became equal to rate of recharge. He presented two formulas one for steady radial flow in unconfined aquifer and other for steady radial flow in a confined aquifer. In doing so he made quite a few assumptions to simplify the matter.

The assumptions are:

(i) The velocity of flow is proportional to the tangent of the hydraulic gradient rather than the sine as determined by Darcy.

(ii) The flow is horizontal and uniform everywhere in a vertical section.

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(iii) The aquifer is homogeneous, isotropic and of infinite areal extent so that coefficient of permeability is constant everywhere,

(iv) The well penetrates fully and it receives water from the entire thickness of the aquifer.